Macario, who played for Hayes at Chelsea in the English Women's Super League, had only returned in March from a long-term knee injury.
Hayes, who said she was "gutted" by the news, said the injury was "not a long-term situation, (she's) just not going to recover in time for the Olympics".
"She trained the other day, but she had some irritation leading up to that and it reacted," Hayes told a news conference.
"Having been through the last 12 months with her, I know it's complex. So her welfare comes first and as I said, she's done everything she can and she's devastated," added Hayes.
Lynn Williams, who had been named as a reserve in the squad, will step upin place of Macario.
The USA won Olympic gold in 1996, 2004, 2008 and 2012 and warm up for the Paris Games with a friendly against Mexico on Saturday and then a meeting with Costa Rica in Washington DC, on Tuesday.
Their opening game at the Olympics, in Group B, will be against Zambia in Nice on July 25.
Hayes' team will also face Germany and Australia in the group stage.
